Secondary batteries generate electric energy by electrochemical oxidation and reduction reactions, and have been widely used for various purposes. For example, secondary batteries are used in gradually expanding applications including: portable devices such as mobile phones, laptop computers, digital cameras, video cameras, tablet computers, and electrically-drive tools; various electrically-driven power units such as electric bicycles, electric motorcycles, electric vehicles, hybrid vehicles, electric ships, and electric aircrafts; power storage devices used to store surplus power or power generated by new and renewable energy; uninterruptible power supplies for stably supplying power to various information communication devices including server computers and communication base stations; and the like.
Generally, a secondary battery has a structure in which an electrode assembly and an electrolyte are sealed in a packaging material and two electrode terminals having different polarities are exposed outside the packaging material. The electrode assembly includes a plurality of unit cells, and the unit cells have a structure in which a porous separator is interposed at least between a negative electrode plate and a positive electrode plate. The negative electrode plate and the positive electrode plate are coated with active materials involved in electrochemical reactions, and the secondary battery is charged or discharged by electrochemical reactions between the active materials and the electrolyte.
The capacity of a secondary battery is not continuously maintained at the capacity at beginning of life (BOL), and is reduced as a calendar time or cycle time elapses. The calendar time refers to cumulative time for which a secondary battery maintains a no-load state, and the cycle time refers to cumulative time for which a secondary battery maintains a charge or discharge state. Capacity reduction of a secondary battery may be quantitatively calculated by a degree of aging (DOA). The degree of aging may be defined by a ratio of a currently reduced amount of the capacity to the capacity at BOL. A degree of aging is a measure indicating a replacement cycle of a secondary battery. That is, since it is meant that the capacity of a secondary battery is significantly reduced if the degree of aging is above a critical value, the secondary battery needs to be replaced.
Aging of a secondary battery proceeds while the secondary battery is in a no-load state, that is, a calendar state, as well as in a charge-discharge state, that is, a cycle state. The reason is that, even though a secondary battery is in a no-load state, the capacity of the secondary battery is reduced due to reasons such as irreversible deformation of an electrolyte and an active material coated on an electrode, or an increase of the thickness of a solid electrolyte interphase (SEI) layer formed on a surface of an anode.
In addition, the aging of a secondary battery is faster in a cycle state than in a calendar state. The reason is that, when a secondary battery is in a cycle state, Joule heat is generated while a charge or discharge current flows, and that irreversible deformation of an active material and an electrolyte more quickly proceeds while operation ions (Li ions in the case of lithium batteries) are intercalated to or deintercalated from an electrode.
A degree of aging of a secondary battery may be determined by measuring the capacity of the secondary battery and calculating how much difference the measured capacity has with reference to the BOL capacity of the secondary battery.
For reference, the capacity of a secondary battery may be calculated by integrating a charge current flowing in the secondary battery while the secondary battery is charged to a state of charge (SOC) of 100% upon complete discharge of the secondary battery.
However, there are few cases in which a secondary battery is completely discharged in actual usage environments of the secondary battery, and it is difficult to accurately determine the capacity of the secondary battery due to an error of a current sensor.
Therefore, in a technical field to which the present disclosure pertains, various methods of indirectly estimating a degree of aging of a secondary battery have been developed, and one of the methods is a method using a degree-of-aging integration model.
In the degree-of-aging integration model, as shown in FIG. 1, a plurality of degree-of-aging profiles Δγ1(t), Δγ2(t) . . . Δγn(t) are predefined depending upon an operation condition of a secondary battery, for example, a state of charge (SOC), a temperature, a C-rate, or the like.
In addition, in the degree-of-aging integration model, while a secondary battery is operated, an operation condition is identified and a degree-of-aging profile corresponding to the identified operation condition is selected, and while the operation condition is maintained, a change in a degree of aging of the secondary battery is determined by using the identified degree-of-aging profile. Further, in the degree-of-aging integration model, the degree of aging at a current point of time is determined by integrating the determined change in the degree of aging of the secondary battery whenever the operation condition is changed.
Referring to FIG. 1, for example, when a secondary battery, which is aged little and is in a BOL state, maintains a cycle state for a time Δt1 under a specific operation condition and a degree-of-aging profile corresponding to the operation condition is a curve Δγn-k(t), where 1≤k≤n−1, the degree of aging of the secondary battery increases from 0% corresponding to a point P0 to G1% corresponding to a point P1 along a solid-line-marked portion of the curve Δγn-k(t). That is, the degree of aging of the secondary battery is increased by G1% for the time Δt1.
When the time Δt1 has elapsed, if the operation condition of the secondary battery is changed and a degree-of-aging profile corresponding to the changed operation condition is a curve Δγ2(t), the degree of aging of the secondary battery after the time Δt1 increases along the curve Δγ2(t). However, since the degree of aging needs to consecutively increase, a position of time at which calculation of the degree of aging starts under the changed operation condition is changed from the point P1 to a point P2. Hereinafter, in a changed degree-of-aging profile, time that is a reference for an increase of the degree of aging, such as the point P2, is referred to as reference equivalent time. If the changed operation condition is maintained for a time Δt2, the degree of aging of the secondary battery increases from G1% corresponding to the point P2 to G2% corresponding to a point P3 along a solid-line-marked portion of the curve Δγ2(t). Therefore, the degree of aging of the secondary battery is increased by (G2−G1)% for the time Δt2, and the current degree of aging is G2% when a change in the degree of aging is integrated with the previous degree of aging of G1%.
Furthermore, when a time Δt1+Δt2 has elapsed, if the operation condition of the secondary battery is changed again and a degree-of-aging profile corresponding to the changed operation condition is a curve Δγ1(t), the degree of aging of the secondary battery increases along the curve Δγ1(t) after the time Δt1+Δt2. However, since the degree of aging needs to consecutively increase, the reference equivalent time on the curve Δγ1(t) is changed to time corresponding to a point P4. If the changed operation condition is maintained for a time Δt3, the degree of aging of the secondary battery increases from G2% corresponding to the point P4 to G3% corresponding to a point P5 along a solid-line-marked portion of the curve Δγ1(t). Therefore, the degree of aging of the secondary battery is increased by (G3−G2)% for the time Δt3, and the current degree of aging is G3% when such a change in the degree of aging is integrated with the previous degree of aging of G2%.
As such, a process of changing the degree-of-aging profile when the operation condition of the secondary battery is changed, a process of determining the reference equivalent time, which corresponds to an immediately previously integrated degree of aging, on the changed degree-of-aging profile, a process of determining an increment of the degree of aging of the secondary battery by using the changed profile while the changed operation condition is maintained, and a process of updating the degree of aging by integrating the increment of the degree of aging with the immediately previous degree of aging are continuously repeated.
However, since, in a conventional degree-of-aging integration model, a change in a degree of aging is integrated without separately distinguishing the case that a secondary battery is in a cycle state from the case that the secondary battery is in a calendar state, there is a problem of estimating the degree of aging lower than it actually is. The reason is that, since a slope change of a changed degree-of-aging profile is suddenly reduced if reference equivalent time of the changed degree-of-aging profile is suddenly increased, the change in the degree of aging is calculated to be lower than it actually is.
For example, in the example set forth above, if, when the time Δt1 has elapsed, the operation condition of the secondary battery is changed and the degree-of-aging profile used in calculation of the degree of aging is changed from the curve Δγn-k(t) to a curve Δγn(t) having the most gentle slope, the reference equivalent time is suddenly increased to time corresponding to a point P6.
The curve Δγn(t) has a more gentle profile slope than any other curves. Therefore, even though the operation condition corresponding to the curve Δγn(t) is maintained for a relatively long time Δt4, since the degree of aging of the secondary battery is increased only to a degree of aging corresponding to a point P7, a change in the degree of aging is significantly smaller than a change in time. Therefore, as the degree of aging is integrated by using a degree-of-aging profile having a smaller slope change, an estimation error of the degree of aging is further increased since the change in the degree of aging is calculated to be lower than it actually is.